【摘要】 应用矢量有限元方法(FEM)对三维电磁问题进行分析,研究应用超松弛迭代(SSOR)方法预处理的双共轭梯度(BICG)求解有限元线性方程组的收敛特性.文中给出了SSOR-BICG方法的高效算法,并对三维腔体的电磁散射问题和三维波导不连续性结构进行了分析.研究表明,通过SSOR预处理,在不增加内存消耗的情况下,有限元系数矩阵性态大为改善,BICG求解速度大大提高.SSOR-BICG方法在计算时间上比BICG方法和共轭梯度法(CG)分别可以提高了4倍和44倍,从而为电大目标的有限元方法快速分析提供技术支持.更多还原

【Abstract】 Vector finite-element method(FEM) is applied for the analysis of 3D electromagnetic field boundary value problems,then,the application of symmetric successive overrelaxation(SSOR) preconditioned Biconjugate-gradient(BICG) method is investigated for solving the resulting linear equations.The efficient SSOR-BICG implementation is presented for complex coefficient matrix.The matrix condition is improved evidently with the preconditioning matrix that is structured with no additional computational time and storage.The SSOR-BICG can reach convergence nearly 4 times faster and 44 times faster than that of BICG and conjugate-gradient(CG) respectively in CPU time for some typical structures.The presented numerical results demonstrate that,when vector FEM is employed to analyze 3-D electromagnetic-field problems,the SSOR-BICG method is efficient for solving the resulting large-scale FEM equations.更多还原